Defining parameters
| Level: | \( N \) | = | \( 4 = 2^{2} \) |
| Weight: | \( k \) | = | \( 16 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(16\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(4))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 9 | 1 | 8 |
| Cusp forms | 6 | 1 | 5 |
| Eisenstein series | 3 | 0 | 3 |
Trace form
Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(4))\)
We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.
| Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
|---|---|---|---|---|
| 4.16.a | \(\chi_{4}(1, \cdot)\) | 4.16.a.a | 1 | 1 |
Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(4))\) into lower level spaces
\( S_{16}^{\mathrm{old}}(\Gamma_1(4)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)